中国物理B ›› 2002, Vol. 11 ›› Issue (3): 266-271.doi: 10.1088/1009-1963/11/3/313

• CONDENSED MATTER: STRUCTURAL, MECHANICAL, AND THERMAL PROPERTIES • 上一篇    下一篇

Elastic analysis of a mode II crack in a decagonal quasi-crystal

李显方1, 范天佑2   

  1. (1)College of Science, Hunan Normal University, Changsha, Hunan 410081, China; (2)Department of Applied Physics, Beijing Institute of Technology, Beijing 100081, China
  • 收稿日期:2001-06-01 修回日期:2001-11-06 出版日期:2005-06-13 发布日期:2005-06-13
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant No 19972011).

Elastic analysis of a mode II crack in a decagonal quasi-crystal

Li Xian-Fang (李显方)a, Fan Tian-You (范天佑)b   

  1. a College of Science, Hunan Normal University, Changsha, Hunan 410081, China; b Department of Applied Physics, Beijing Institute of Technology, Beijing 100081, China
  • Received:2001-06-01 Revised:2001-11-06 Online:2005-06-13 Published:2005-06-13
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant No 19972011).

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摘要： The elastic analysis of a mode II Griffith crack penetrating through a decagonal quasi-crystal along the periodic axis is made within the context of the continuum theory. By using a general solution obtained previously, the problem in the case of uniform shear stress at infinity is solved, and the analytical expressions for the entire stress field disturbed by an internal crack are derived in an explicit form. The asymptotic fields of the displacement and stress around a crack tip in both phonon and phason fields indicate that the stresses near a crack tip exhibit the square-root singularity. The formula for evaluating the energy release rate is also given. If imposing that the phason field is absent, the well-known results of a mode II crack in a conventional material are recovered from the present results.

Abstract: The elastic analysis of a mode II Griffith crack penetrating through a decagonal quasi-crystal along the periodic axis is made within the context of the continuum theory. By using a general solution obtained previously, the problem in the case of uniform shear stress at infinity is solved, and the analytical expressions for the entire stress field disturbed by an internal crack are derived in an explicit form. The asymptotic fields of the displacement and stress around a crack tip in both phonon and phason fields indicate that the stresses near a crack tip exhibit the square-root singularity. The formula for evaluating the energy release rate is also given. If imposing that the phason field is absent, the well-known results of a mode II crack in a conventional material are recovered from the present results.

Key words: quasi-crystal, crack, elastic field, energy release rate, singularity

中图分类号:  (Structural failure of materials)

  • 62.20.M-
46.50.+a (Fracture mechanics, fatigue and cracks) 61.44.Br (Quasicrystals)